document.write( "Question 77523This question is from textbook Algebra 2
\n" ); document.write( ": Can someone please help me with this problem?\r
\n" ); document.write( "\n" ); document.write( "Find a1 in a geometric series for which Sn=189, r=1/2, and an=3. \n" ); document.write( "
Algebra.Com's Answer #55626 by Edwin McCravy(20056)\"\" \"About 
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document.write( "Can someone please help me with this problem? \r\n" );
document.write( "Find a1 in a geometric series for which \r\n" );
document.write( "Sn=189, r=1/2, and an=3.\r\n" );
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document.write( "an = a1rn-1\r\n" );
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document.write( "an = a1(1/2)n-1\r\n" );
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document.write( "3 = a1(1/2n-1)\r\n" );
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document.write( "3(2n-1) = a1\r\n" );
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document.write( "      a1(1 - rn)\r\n" );
document.write( "Sn = ------------\r\n" );
document.write( "        1 - r  \r\n" );
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document.write( "Sn = a1(1/2)n-1\r\n" );
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document.write( "       a1[1 - (1/2)n]\r\n" );
document.write( "189 = ----------------\r\n" );
document.write( "         1 - 1/2\r\n" );
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document.write( "Simplifying the second\r\n" );
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document.write( "       a1[1 - 1/2n]\r\n" );
document.write( "189 = --------------\r\n" );
document.write( "           1/2\r\n" );
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document.write( "       a1(1 - 2-n)\r\n" );
document.write( "189 = -------------\r\n" );
document.write( "           1/2\r\n" );
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document.write( "Multiply the numerator and \r\n" );
document.write( "denominator on the right by 2\r\n" );
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document.write( "189 = 2a1(1 - 2-n) \r\n" );
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document.write( "Since 3(2n-1) = a1, substitute 3(2n-1) for a1 \r\n" );
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document.write( "189 = 2[3(2n-1)](1 - 2-n)\r\n" );
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document.write( "189 = 3(21)(2n-1)(1 - 2-n)\r\n" );
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document.write( "189 = 3(2n)(1 - 2-n)\r\n" );
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document.write( "Divide both sides by 3\r\n" );
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document.write( "63 = 2n(1 - 2-n)\r\n" );
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document.write( "Distribute\r\n" );
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document.write( "63 = 2n - 2n-n\r\n" );
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document.write( "63 = 2n - 20\r\n" );
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document.write( "63 = 2n - 1\r\n" );
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document.write( "64 = 2n\r\n" );
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document.write( "26 = 2n\r\n" );
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document.write( "6 = n\r\n" );
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document.write( "3(2n-1) = a1\r\n" );
document.write( "3(26-1) = a1\r\n" );
document.write( "3(25) = a1\r\n" );
document.write( "  3(32) = a1\r\n" );
document.write( "     96 = a1\r\n" );
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document.write( "To check, start with 96 and multiply by 1/2 until \r\n" );
document.write( "we have 6 terms:\r\n" );
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document.write( "96, 48, 24, 12, 6, 3\r\n" );
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document.write( "So the nth or 6th term, an = a6 = 3.  That checks.\r\n" );
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document.write( "Sn = S6 = 96+48+24+12+6+3 = 189.  That checks.\r\n" );
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document.write( "Edwin
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